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Nonlinear Dynamics

, Volume 77, Issue 4, pp 1223–1236 | Cite as

Complex dynamic behavior in a viral model with state feedback control strategies

  • Lin-Fei Nie
  • Zhi-Dong Teng
  • Il Hyo Jung
Original Paper

Abstract

With the consideration of mechanism of prevention and control for the spread of viral diseases, in this paper, we propose two novel virus dynamics models where state feedback control strategies are introduced. The first model incorporates the density of infected cells (or free virus) as control threshold value; we analytically show the existence and orbit stability of positive periodic solution. Theoretical results imply that the density of infected cells (or free virus) can be controlled within an adequate level. The other model determines the control strategies by monitoring the density of uninfected cells when it reaches a risk threshold value. We analytically prove the existence and orbit stability of semi-trivial periodic solution, which show that the viral disease dies out. Numerical simulations are carried out to illustrate the main results.

Keywords

Virus dynamics model State feedback control Positive periodic solution Semi-trivial periodic solution Orbital stability 

Notes

Acknowledgments

The authors would like to thank antonymous referees for their constructive suggestions and comments that substantially improved the original manuscript. This research has been partially supported by the National Natural Science Foundation of China (Grant Nos. 11001235, 11271312, and 11261056), the China Postdoctoral Science Foundation (Grant Nos. 20110491750 and 2012T50836), and the Natural Science Foundation of Xinjiang (Grant No. 2011211B08).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityUrumqiPeople’s Republic of China
  2. 2.Department of MathematicsPusan National UniversityBusanRepublic of Korea

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